Lattice NRQCD at non-zero temperature Seyong Kim Sejong University - - PowerPoint PPT Presentation

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Lattice NRQCD at non-zero temperature Seyong Kim Sejong University - - PowerPoint PPT Presentation

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion Lattice NRQCD at non-zero temperature Seyong Kim Sejong University in collaboration with G. Aarts(Swansea), C. Allton(Swansea), S. Hands(Swansea), M.P . Lombardo(LNF), M.B.

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Lattice NRQCD at non-zero temperature

Seyong Kim

Sejong University

in collaboration with

  • G. Aarts(Swansea), C. Allton(Swansea), S. Hands(Swansea),

M.P . Lombardo(LNF), M.B. Oktay(Utah), S.M. Ryan(Trinity), D.K. Sinclair(ANL), J.I. Skullerud (NUIM) based on PRL106, (2011) 061602 arXiv:1010.3752, JHEP1111, (2011) 103 arXiv:1109.4496, and arXiv:1210.2903 and PLB 711, (2012) 199 arXiv:1202.4353

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Outline

1

Introduction

2

Lattice NRQCD

3

Lattice NRQCD at T = 0

4

Conclusion

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Lattice Gauge Theory

  • lattice gauge theory aims to calculate low energy non-perturbative

quantities in QCD reliably and quantitatively.

  • despite the systematic errors from finite lattice spacing, finite

spacetime volume, finite quark mass

  • cf. K.G. Wilson, PRD10 (1974) 2445

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Lattice Gauge Theory

2012 PDG summary on QCD

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Lattice NRQCD

  • NRQCD is an effective field theory
  • expansion in v, the heavy quark velocity in heavy quarkonium
  • Ma ∼ 1
  • quarkonium spectrum is one of “gold plated” result from lattice QCD

(PRL 92 (2004) 022001 )

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Lattice NRQCD

  • Non-relativistic QCD

G(

  • x,t = 0)

=

S(x) (1) G(

  • x,t = 1)

=

  • 1+ 1

2n

  • D2

2m0

b

n

U†

4(

  • x,t)
  • 1+ 1

2n

  • D2

2m0

b

n

G(

  • x,0)

(2) G(

  • x,t + 1)

=

  • 1+ 1

2n

  • D2

2m0

b

n

U†

4(

  • x,t)
  • 1+ 1

2n

  • D2

2m0

b

n [1−δH]G(

  • x,t)

(3)

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Lattice NRQCD

where S(x) is the source and

δH = −(

D(2))2 8(m0

b)3 +

ig 8(m0

b)2 (

D · E − E · D)

−

g 8(m0

b)2

σ·(

D × E − E × D)− g 2m0

b

  • σ·

B

+

a2 D(4) 24m0

b

− a(

D(2))2 16n(m0

b)2

(1)

  • calculate NRQCD propagator using gluon field which has light quark

vacuum polarization effect

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Non-zero T on lattice

  • N3

s × Nτ lattice, T = 1 Nτa

  • boundary condition for quantum field on the time direction
  • high temperature means Nt << Ns → spectrum in finite temperature

environment is not feasible

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Lattice study of quarkonium in non-zero T

  • T
  • few times nuclear

matter density

µ µ

T

  • color

superconductor hadron gas confined,

χ-SB

quark-gluon plasma deconfined,

χ-symmetric

  • 9 / 47
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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Lattice study of quarkonium in non-zero T

  • Recall Schroedinger eq.

i ∂ψ

∂t = H ψ

(2) with H = 2M − ∇2

2M + V(r)

  • T = 0, e.g., Cornel potential;

V(r) = −α r +σr (3)

  • T = 0, Debye screening;

V(r,T) =

σ µ(T)(1− e−µ(T)r)− α

r e−µ(T)r (4) where µ(T) = 1/rD(T)

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Lattice study of quarkonium in non-zero T

  • F. Karsch, M.T. Mehr, and H. Satz, Z.Phys.C37 (1988) 617.

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Lattice study of quarkonium in non-zero T

  • separation of scale: M (heavy quark mass) and Mv (bound state

momentum)

  • decay rate = the probability for heavy quark and heavy anti-quark to

meet × partonic cross-section for quark–anti-quark annihilation

  • similar to positronium

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Lattice study of quarkonium in non-zero T

  • obtain finite temperature heavy quark potential by lattice calculation

→ solve Schroedinger equation

  • obtain spectral function of heavy meson correlator by lattice

calculation → observe temperature modification of spectrum

  • “derive” potential from Wilson loop
  • study heavy quarkonium correlator in finite temperature by lattice

NRQCD on anisotropic lattice

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Anisotropic lattice study of quarkoinum in non-zero T

  • choose the time direction lattice spacing aτ different from the space

direction lattice spacing as

  • more lattice points along the temperature direction (or time direction)

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Anisotropic lattice study of quarkoinum in non-zero T

  • Anisotropic lattice on 123 × Nt (ref. G. Aarts et al, PRD 76 (2007)

094513) Ns Nt a−1

τ

T(MeV) T/Tc

  • No. of Conf.

12 80 7.35GeV 90 0.42 250 12 32 7.35GeV 230 1.05 1000 12 28 7.35GeV 263 1.20 1000 12 24 7.35GeV 306 1.40 500 12 20 7.35GeV 368 1.68 1000 12 18 7.35GeV 408 1.86 1000 12 16 7.35GeV 458 2.09 1000

Table: summary for the lattice data set

  • two-plaquette Symanzik improved gauge action, fine-Wilson,

coarse-Hamber-Wu fermion action with stout-link smearing

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Anisotropic lattice study of quarkoinum in non-zero T

  • bound state → exponential decay of the propagator

G(τ) ∼ Ae−Eτ (2)

  • free state → power-like decay

G(τ) ∼ A′τ−γ (3)

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Effective mass for Υ

meff(τ) = −log[G(τ)/G(τ− aτ)], (4)

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Effective mass for Υ

20 40 60 80

τ/aτ

0.1 0.15 0.2 0.25

aτmeff

T=0.42Tc T=1.05Tc T=1.40Tc T=2.09Tc 1

3S1 (Υ) 18 / 47

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Effective mass for χb1

20 40 60 80

τ/aτ

0.15 0.25 0.35 0.45

aτmeff

T=0.42Tc T=1.05Tc T=1.40Tc T=2.09Tc 1

3P1 (χb1) 19 / 47

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

χb propagator

2 4 8 16

τ/aτ

0.1 1 10

G(τ)

χb0 χb1 χb2 T=2.09Tc

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

effective exponent for Υ

γeff(τ) = −τG′(τ)

G(τ) = −τG(τ+ aτ)− G(τ− aτ) 2aτG(τ) (4)

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

effective exponent for Υ

8 16 24 32

τ/aτ

1 2 3 4 5

γ eff

T=0.42Tc T=1.05Tc T=1.40Tc T=2.09Tc free field 1

3S1 (Υ) 22 / 47

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

effective exponent for χb

8 16 24 32

τ/aτ

1 2 3 4 5 6 7

γ eff

T=0.42Tc T=1.05Tc T=1.40Tc T=2.09Tc free field 1

3P1 (χb1) 23 / 47

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

S-wave bottomonium spectral function

GΓ(τ)

= ∑

  • x

ψ(τ,

x)Γψ(τ, x)ψ(0, 0)Γψ(0, 0) (4)

=

  • d3p

(2π)3

∞ dω 2π K(τ,ω)ρΓ(ω, p) (5) and K(τ,ω) = cosh[ω(τ− 1/2T)] sinh(ω/2T)

.

(6) With ω = 2M +ω′ and T/M << 1, G(τ) = ∞

−2M

dω′ 2π exp(−ω′τ)ρ(ω′) (7)

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

S-wave bottomonium spectral function

9 10 11 12 13 14 15

ω [GeV]

5 10 15 20

ρ(ω)/M

2

9 10 11 12 13 14 1 2 3S1(vector)

T/Tc=0.42 Upsilon

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

S-wave bottomonium spectral function

ω [GeV]

1 2 3

ρ(ω)/M

2

T/Tc=0.42 T/Tc=1.05 T/Tc=1.05 T/Tc=1.20 T/Tc=1.20 T/Tc=1.40

9 10 11 12 13 14 1 2

T/Tc=1.40 T/Tc=1.68

9 10 11 12 13 14

T/Tc=1.68 T/Tc=1.86

9 10 11 12 13 14 15

T/Tc=1.86 T/Tc=2.09

3S1(vector)

Upsilon

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

S-wave bottomonium spectral function

9 10 11 12 13 14 15

ω [GeV]

5 10 15 20

ρ(ω)/M

2

9 10 11 12 13 14 1 2 1S0(pseudoscalar)

T/Tc=0.42 ηb

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

S-wave bottomonium spectral function

ω [GeV]

1 2 3

ρ(ω)/M

2

T/Tc=0.42 T/Tc=1.05 T/Tc=1.05 T/Tc=1.20 T/Tc=1.20 T/Tc=1.40

9 10 11 12 13 14 1 2

T/Tc=1.40 T/Tc=1.68

9 10 11 12 13 14

T/Tc=1.68 T/Tc=1.86

9 10 11 12 13 14 15

T/Tc=1.86 T/Tc=2.09

1S0(pseudoscalar)

ηb

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

S-wave bottomonium spectral function

0.5 1 1.5 2

T/Tc

0.15 0.16 0.17 0.18 0.19

∆E/M

3S1(vector)

Upsilon

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

S-wave bottomonium spectral function

0.5 1 1.5 2

T/Tc

0.5 1 1.5 2

Γ/T

3S1(vector)

Upsilon

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

S-wave bottomonium spectral function

0.5 1 1.5 2

T/Tc

0.15 0.16 0.17 0.18 0.19

∆E/M

1S0(pseudoscalar)

ηb

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

S-wave bottomonium spectral function

0.5 1 1.5 2

T/Tc

0.5 1 1.5 2

Γ/T

1S0(pseudoscalar)

ηb

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

S-wave bottomonium spectral function

0.2 0.4 0.6 0.8 1

aτω

0.5 1 1.5

aτ

2ρ(ω)

m(ω) = 0.014 m(ω) = 0.14 * m(ω) = 1.4 m(ω) = 0.018 m(ω) = 0.18 √ω−ωmin * m(ω) = 1.8 √ω−ωmin

3S1(vector)

Nτ=32 Upsilon

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

S-wave bottomonium spectral function

0.25 0.5 0.75 1

aτω

0.5 1

aτ

2ρ(ω)

m(ω) = 0.011 m(ω) = 0.11 * m(ω) = 1.1 m(ω) = 0.013 √ω−ωmin m(ω) = 0.13 √ω−ωmin * m(ω) = 1.3 √ω−ωmin

3S1(vector)

Nτ=16 Upsilon

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

S-wave bottomonium spectral function

0.04 0.08 0.12 0.16 1/√Ncfgs 0.11 0.13 0.15 0.17

aτ∆E

Nτ=32 Nτ=28 Nτ=20 Nτ=16

(points shifted horizontally for clarity) 3S1(vector) Upsilon

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

S-wave bottomonium spectral function

0.04 0.08 0.12 0.16 1/√Ncfgs 0.05 0.1 0.15

aτΓ

Nτ=32 Nτ=28 Nτ=20 Nτ=16

(points shifted horizontally for clarity) 3S1(vector) Upsilon

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

S-wave bottomonium spectral function

0.2 0.4 0.6 0.8 1

aτω

0.25 0.5 0.75 1

aτ

2ρ(ω)

τ2/aτ=12 τ2/aτ=14 τ2/aτ=16 τ2/aτ=17 τ2/aτ=18 τ2/aτ=19

3S1(vector)

Upsilon Nτ=20

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

S-wave bottomonium spectral function

0.2 0.4 0.6 0.8

aτω

0.25 0.5 0.75 1

aτ

2ρ(ω)

τ2/aτ=8 τ2/aτ=10 τ2/aτ=12 τ2/aτ=13 τ2/aτ=14 τ2/aτ=15

3S1(vector)

Nτ=16 Upsilon

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

S-wave bottomonium spectral function

0.06 0.12 0.18

[τ2/aτ]

−1

0.11 0.13 0.15 0.17

aτ∆E

Nτ=80 Nτ=32 Nτ=28 Nτ=20 Nτ=16 window: τ = [aτ,...,τ2]

3S1(vector) Upsilon

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

S-wave bottomonium spectral function

0.06 0.12 0.18

[τ2/aτ]

−1

0.05 0.1 0.15

aτΓ

Nτ=80 Nτ=32 Nτ=28 Nτ=20 Nτ=16

3S1(vector) Upsilon

window: τ = [aτ,...,τ2]

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

CMS collaboration, PRL107 (2011) 052302

ω [GeV]

1 2 3

ρ(ω)/M

2

T/Tc=0.42 T/Tc=1.05 T/Tc=1.05 T/Tc=1.20 T/Tc=1.20 T/Tc=1.40

9 10 11 12 13 14 1 2

T/Tc=1.40 T/Tc=1.68

9 10 11 12 13 14

T/Tc=1.68 T/Tc=1.86

9 10 11 12 13 14 15

T/Tc=1.86 T/Tc=2.09

3S1(vector)

Upsilon

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

CMS collaboration, PRL107 (2011) 052302

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

CMS collaboration, PRL107 (2011) 052302

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Upsilon moving in a thermal bath

  • 0.2

0.2 0.4 0.6 0.8 1 ω 50 100 150 200 250 300 ρ(ω) 12x20 p=000 12x20 p=100 12x20 p=110 12x20 p=111 12x20 p=200 12x20 p=210 12x20 p=211 12x20 p=220

NRQCD_20n sonia_20n_ spp_i_000 K=.00000,.00000 # 2

t = 1-19 Err=J Sym=N #cfgs=1000 #cfg/clus= 1

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Upsilon moving in a thermal bath

  • observable heavy quarkonium velocity (

v2

Upsilon

c2

∼ 0.03) effect on the

S-wave state mass (NR dispersion ∼

  • p2

2MUpsilon )

2 4 6 8 |plat

2 a 2|

0.11 0.12 0.13 0.14 0.15 ∆E 12x16 12x18 12x20 12x24 12x28 12x32 12x80

Upsilon

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Upsilon moving in a thermal bath

  • no observable v2

Upsilon effect on the S-wave state “width” (Escobedo

et al., PRD84 (2011) 016008, Γv/Γ0 ∼ 1− 2

3v2

Upsilon) 2 4 6 8 |plat

2 a 2|

0.02 0.04 0.06 0.08 width 12x16 12x18 12x20 12x24 12x28 12x32 12x80

Upsilon

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Introduction Lattice NRQCD Lattice NRQCD at T = 0 Conclusion

Conclusion

  • lattice NRQCD method for bottomonium on anisotropic lattice offers

a method which is systematically improvable and is based on the first principel of quantum field theory (not a model)

  • lattice NRQCD at zero temperature already produced accurate result

and is producing more accurate result

  • Υ and ηb (S-wave) show that the ground state survives but the

excited states are suppressed as the temperature increases above Tc.

  • χb (P-wave) follows a power-law decay at T = 1.4Tc and is nearly

consistent with free dynamics at T = 2.09Tc. This means that unlike S-wave, P-wave melts almost immediately above Tc

  • further studies on bottomonium (including systematic error study)

are under way.

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